Freak Waves as a Result of Modulational Instability
Abstract
We have studied numerically the development of modulational instability for stationary propogating Stokes waves of a moderate magnitude, (k_{a=0.15}), on a deep water. The spectral code method was applied to exact onedimensional hydrodynamic equations, which describe the porential flow of an ideal fluid with free surface; this surface was conformlly mapped to the half plane. The equations were solved in a box with periodic boundary conditions containing as much as ten lengths of the leading wave. The total amount of spectral modes were varied between 3ṡ 10^{4} to 1ṡ 10^{6}. In the initial moment of time, the exact Stokes wave was modulated by a small long scale perturbation. As a result, we observed an exponential growth of modulation, which was leading to the formation of a single freak wave. The freak wave grew up to the limiting amplitude of (k_{a ∼} 0.45); then, it demonstrated a tendency to an explosive formation of singularity.
 Publication:

AGU Spring Meeting Abstracts
 Pub Date:
 May 2004
 Bibcode:
 2004AGUSMOS14A..04Z
 Keywords:

 4560 Surface waves and tides (1255);
 4572 Upper ocean processes